Question

Calcule a derivada de f(x)=In(x)/x

Answer 1

usando a regra do quociente

$\boxed{\boxed{\left( \frac{U}{V} \right)' = \frac{U*V'-U*V'}{V^2} }}$

aplicando isso no problema
$f(x)= \frac{ln(x)}{x} \\\\ f'(x)= \frac{[ln(x)]'*x - ln(x)*[x]'}{x^2} \\\\f'(x)= \frac{[ \frac{1}{x} ]*x-ln(x)*[1]}{x^2} \\\\f'(x)= \frac{ 1-ln(x) }{x^2}$